Problem: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}3x-8y &= -2 \\ 7x-7y &= 7\end{align*}$
Answer: Begin by moving the $x$ -term in the second equation to the right side of the equation. $-7y = -7x+7$ Divide both sides by $-7$ to isolate $y$ $y = {x - 1}$ Substitute this expression for $y$ in the first equation. $3x-8({x - 1}) = -2$ $3x - 8x + 8 = -2$ Simplify by combining terms, then solve for $x$ $-5x + 8 = -2$ $-5x = -10$ $x = 2$ Substitute $2$ for $x$ back into the top equation. $3( 2)-8y = -2$ $6-8y = -2$ $-8y = -8$ $y = 1$ The solution is $\enspace x = 2, \enspace y = 1$.